IN A NUTSHELL:Nobody. The footage of the liftoff of the Lunar Module from the Moon was shot using an independently powered TV camera that was radio controlled from Earth.

THE DETAILS: The visual record of the Apollo missions includes footage of the liftoff of the Lunar Module from the Moon. Some conspiracy theorists and doubters argue that this video must be fake, since there was nobody left on the Moon to take the pictures and even move the camera to follow the ascent stage of the Lunar Module as it climbed into the sky.

The answer is simple: the liftoff was shot only during Apollo 15, 16 and 17, when the TV camera was installed on the Rover (the astronauts' electric car), which at the end of the excursion was parked approximately 90 meters (300 feet) east of the Lunar Module for the very purpose of recording the liftoff of the LM. The camera was controlled remotely by an operator on Earth. Indeed, its technical name was GCTA, which stands for Ground Controlled Television Assembly.

Figure 6-13. Apollo 17: a still from the live TV broadcast
of the liftoff of the LM ascent stage from the Moon.

Figure 6-14. Animation of how the LM liftoff videos were shot.
From the documentary Live from the Moon (Spacecraft Films).

The signal from the TV camera left on the Moon was transmitted directly to Earth through the parabolic antenna installed on the Rover, using the same method used to transmit the astronauts' moonwalks.

The entire system was powered independently by batteries and therefore was able to transmit even after the astronauts had left the Moon, sending back lonely images of the moonscape, once again devoid of life and motion after humankind's brief visit.